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We propose a computational framework for simulating the self-similar regime of turbulent Rayleigh–Taylor (RT) mixing layers in a statistically stationary manner. By leveraging the anticipated self-similar behaviour of RT mixing layers, a transformation of the vertical coordinate and velocities is applied to the Navier–Stokes equations (NSE), yielding modified equations that resemble the original NSE but include two sets of additional terms. Solving these equations, a statistically stationary RT (SRT) flow is achieved. Unlike temporally growing Rayleigh–Taylor (TRT) flow, SRT flow is independent of initial conditions and can be simulated over infinite simulation time without escalating resolution requirements, hence guaranteeing statistical convergence. Direct numerical simulations (DNS) are performed at an Atwood number of 0.5 and unity Schmidt number. By varying the ratio of the mixing layer height to the domain width, a minimal flow unit of aspect ratio 1.5 is found to approximate TRT turbulence in the self-similar mode-coupling regime. The SRT minimal flow unit has one-sixteenth the number of grid points required by the equivalent TRT simulation of the same Reynolds number and grid resolution. The resultant flow corresponds to a theoretical limit where self-similarity is observed in all fields and across the entire spatial domain – a late-time state that existing experiments and DNS of TRT flow have difficulties attaining. Simulations of the SRT minimal flow unit span TRT-equivalent Reynolds numbers (based on mixing layer height) ranging from 500 to 10 800. The SRT results are validated against TRT data from this study as well as from Cabot & Cook (Nat. Phys., vol. 2, 2006, pp. 562–568).
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Sensitivity Analysis of Direct Numerical Simulation of a Spatially Developing Turbulent Mixing Layer to the Domain Dimensions
Abstract Understanding spatial development of a turbulent mixing layer is essential for many engineering applications. However, the flow development is difficult to replicate in physical or numerical experiments. For this reason, the most attractive method for the mixing layer analysis is the direct numerical simulation (DNS), with the most control over the simulation inputs and free from modeling assumptions. On the other hand, the DNS cost often prevents conducting the sensitivity analysis of the simulation results to variations in the numerical procedure and thus, separating numerical and physical effects. In this paper, effects of the computational domain dimensions on statistics collected from DNS of a spatially developing incompressible turbulent mixing layer are analyzed with the focus on determining the domain dimensions suitable for studying the flow asymptotic state. In the simulations, the mixing layer develops between two coflowing laminar boundary layers formed on two sides of a sharp-ended splitter plate of a finite thickness with characteristics close to those of the untripped boundary layers in the experiments by Bell and Mehta, AIAA J., 28(12), 2034 (1990). The simulations were conducted using the spectral-element code Nek5000.
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- Award ID(s):
- 1944568
- PAR ID:
- 10483349
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Verification, Validation and Uncertainty Quantification
- Volume:
- 8
- Issue:
- 3
- ISSN:
- 2377-2158
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4062770
